336 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
downwards terids to grow more slender by reason of the acceleration of the 
movement due to gravity, a vein directed vertically from below upwards, on 
the contrary, tends to grow thicker on account of the retardation due to gravity; 
and since, according to the hypothesis in question, the progressive attenuation 
of the vein directed from above downwards occasions, by virtue of the recip- 
rocal dependence (solidarité) of the divisions, a diminution of length in the 
incipient divisions, the thickening of the vein directed from below upwards 
must, for the same reason, occasion an augmentation of length in the incipient 
divisions; whence it follows that, when the direction of the emission of the 
vein passes progressively from the first of these cases to the second, the inci- 
pient divisions will continue gradually to grow longer. 
As is seen by the number under discussion, from the direction of the descend- 
ing vertical of the vein to the horizontal direction, the lowering of the principal 
sound is inconsiderable, but it becomes considerable from the horizontal direc- 
tion to that of the ascending vertical, which implies that the same shall be the 
case with the lengthening of the incipient divisions. Now, this fact also flows 
from the hypothesis of § 2: in effect, the vertically ascending vein tends to be 
much more thickened, especially towards its upper extremity, on account of the 
gradual annulment of the velocity of the liquid, than the vertically descending 
vein tends to become slender at an equal distance from the contracted section ; 
consequently, and still in virtue of the solidarity of the divisions, when the vein, 
thrown at first in the horizontal direction, continues approaching the ascending 
vertical direction, the suecessive augmentations in length of the incipient divi- 
sions must become much greater than when the vein, quitting the vertically 
descending direction, attains by degrees the horizontal direction. 
‘The facts observed, being thus connected in a necessary manner with the 
hypothesis of § 2, serve reciprocally for confirmation of the latter, and it was to 
them that we had allusion when we said (§ 2) that this hypothesis was sustained 
by the results of experiment. 
§ 31. In terminating the second series, we announced that in the present one, 
after completing what relates to liquid veins, we should treat of figures of equi- 
librium other than the sphere and cylinder, but in order not to give too much 
extension to this memoir, we have decided to reserve the latter subject for an- 
other occasion. 
Novre.—Since the publication of our theory of the constitution of liquid veins, 
as explained at the end of the previous series, the discussion of such veins has 
formed the subject of several successive publications, which we propose briefly 
to recall. 
In 1849 M. Hagen presented to the Academy of Berlin a memoir on the disks 
which are formed at the meeting of two liquid veins, and on the resolution of 
isolated liquid veins into drops, (Poggendortft’s Annalen, vol. lxxviii p. 451.) The 
experiments made by the author on isolated veins conduct him to a law, in re- 
gard to the relations between the length of the continuous part, the discharge 
and the diameter of the orifice, which does not seem to him to coincide with 
those of Savart. We are convinced that the disagreement is but apparent. In 
fact, Savart has only given his laws as approximative; and besides, as we have 
shown, (2d series, § 80,) these laws only constitute limits which the results of 
experiment approach the more closely as, for a definite orifice, the least of the 
discharges employed is stronger, and as, for a less but definite discharge, the 
orifice is smaller. As to the phenomenon of the resolution into isolated masses, 
M. Hagen, who could have no knowledge of our theory, the latter having been 
then too lately published, hazards the conjecture that this resolution is probably 
attributable to the capillary forces. 
